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Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 259
Analysis and Design of Air Intake of Scramjet Engine
for Lower Starting Mach Number
Vatsal Sorathia
Defence Institute of Advance Technology.
Pune(411023), India
Abstract:- This paper proposes an analysis and design of
air intake of scramjet engine for lower starting Mach
number at M=3.5. In the current scenario, there are lots
of researches have been carried out towards the vehicle
with a combined propulsion system for getting high
performance and efficiency while pursuing a very wide
range of operating Mach number. Due to various
propulsion systems, weight reduction is a very
challenging task for this type of vehicle. So if we can
somehow reduce the starting Mach number of scramjet
engine then we can reduce the required propulsion
system, as the bridge between the maximum possible
velocity of the low-speed engine and the scramjet start
velocity. In beginning, the basic geometry of hypersonic
intake with shock structure is given followed by the
theoretical equations of various design parameters at
various sections of the scramjet engine. Next, various
geometries of intake are constructed with a combination
of a different number of ramps and with different ramp
angles. Analysis of intake geometries against lower Mach
number flow is carried out by CFD simulations and
various flow parameters are measured. From these flow
parameters, performance parameters are found and
compare various intake geometries based on them.
Keywords:- Lower starting Mach number, Hypersonic,
Scramjet, Air-intake, Ramp angle, CFD.
Nomenclature T= Static temperature
P= Static pressure
V= Velocity
𝜌 = Density
R=Gas constant
𝐶𝑝=Specific heat
A=Area
f= Fuel to air ratio
𝑓𝑠𝑡= Stoichiometric fuel to air ratio
M= Mach number
𝛾= Ratio of specific heats
∅= Equivalence ratio
S= Specific fuel consumption 𝑉𝑓𝑥
𝑉3=Ratio of Fuel Injection Axial Velocity To Combustor
Entrance Velocity
𝑉𝑓
𝑉3=Ratio of Fuel Injection Total Velocity to Combustor
Entrance Velocity
𝐶𝑓 𝐴𝑤
𝐴3=Burner Effective Drag Coefficient
ℎ𝑃𝑅 = Heat of reaction
ℎ𝑓 =Absolute Sensible Enthalpy of Fuel Entering
Combustor
IT= Ignition temperature
𝑇0 = Reference temperature
𝜂𝑡ℎ = Thermal Efficiency
𝜂𝑝 =Propulsive Efficiency
𝜂𝑐 = Inlet Compression System Efficiency
𝜂𝑏=Burner Efficiency
𝜂𝑒 = Expansion System Efficiency
𝐶𝑝0 =Specific Heat of Freestream Air
𝐶𝑝𝑐 =Specific Heat for Engine Compression
𝐶𝑝𝑏 =Specific Heat for Engine Burner
𝐶𝑝𝑒 =Specific Heat for Engine Expansion
𝛾𝑐= Ratio of Specific Heats for Compression
𝛾𝑏= Ratio of Specific Heats for Burner
𝛾𝑒= Ratio of Specific Heats for Expansion
𝜃 = Ramp angel
𝛽 = Oblique shock angel
𝐹
𝑚0̇= Specific thrust
g= Gravity
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 260
I. INTRODUCTION
In this era of missile propulsion, there are several types
of research are going on scramjet engine technology. It is
the most complex propulsion system in all and there are
many challenges in the development of the scramjet engine
and its application, which I described in the following
discussion. The scramjet engine is the air-breathing engine
and it is working efficiently only at design Mach number
while there are no moving parts in the compression system.
In off-design conditions, it cannot work with its highest
efficiency and sometimes the engine cannot even start. So
now if we talk about the development of some vehicle,
which we want to operate in a large operating Mach number range then we must need more than one propulsion system.
Every propulsion has its own efficient Mach number range
in which it can work in an efficient manner. Figure (1.1.1)
[2]. given below displays a chart of propulsion systems and
their suitable Mach number range. So from this graph, we
can easily get the point that for operating in a wider range
efficiently, then we must include all the required propulsion
systems.
Fig. 1.1.1: Operating Mach number range of different
propulsion systems [2] .
So when a vehicle has more than one propulsion
system, the total weight of the vehicle goes very high. So for getting efficient operation we must take care about weight
reduction. When all the propulsion systems are required, at
that time weight reduction is a very challenging task for the
development of this type of hybrid vehicle. In addition to
this, without weight reduction, we cannot get good payload
carrying capacity up to some realistic limit. If somehow we
can reduce the scramjet starting Mach number then we can
reduce the number of required propulsion systems, as the
gap is fill between the maximum possible velocity of the
low-speed engine and the scramjet start velocity. So this will
ultimately get overall vehicle weight reduction and achieve more payload capacity.
1.2 Scramjet Theory
The equations of different flow parameters at the various designation shown in fig(1.2.1) are given below and
directly taken from [12]:
Fig. 1.2.1: Scramjet reference station designation [12].
𝑀3 = √2
𝛾𝑐−1 {
𝑇0
𝑇3(1 +
𝛾𝑐−1
2 𝑀0
2 ) − 1} (1)
Compression Component (0-3):
Stream thrust function at free stream conditions:
𝑆𝑎0 = 𝑉0 (1 +𝑅𝑇0
𝑉02 ) (2)
Combustor entrance temperature
𝑇3 = ∅𝑇0 (3)
Combustor entrance velocity
𝑉3 = √𝑉02 − 2𝐶𝑝𝑐𝑇0(∅ − 1) (4)
Stream thrust function at combustor entrance
𝑆𝑎3 = 𝑉3 (1 +𝑅𝑇3
𝑉32 ) (5)
Ratio of combustor entrance pressure to free stream
pressure
𝑃3
𝑃0= {
∅
∅(1−𝜂𝑐)+𝜂𝑐}
𝐶𝑝𝑐𝑅
(6)
Ratio of combustor entrance are to free stream
entrance area
𝐴3
𝐴0= ∅
𝑃0
𝑃3
𝑉0
𝑉3 (7)
Combustion Components (3-4):
Combustor exit velocity
𝑉4 = 𝑉3 {1+𝑓
𝑉𝑓𝑥𝑉3
1+𝑓−
𝐶𝑓 𝐴𝑤
𝐴3
2(1+𝑓)} (8)
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 261
Combustor exit temperature
𝑇4 =𝑇3
1+𝑓{1 +
1
𝐶𝑝𝑏𝑇3[𝜂𝑏𝑓ℎ𝑃𝑅 + 𝑓ℎ𝑓 + 𝑓𝐶𝑝𝑏𝑇0 +
(1 + 𝑓𝑉𝑓
2
𝑉32)
𝑉32
2 ]} −
𝑉42
2𝐶𝑝𝑏 (9)
Ratio of area at combustor exit to combustor
entrance
𝐴4
𝐴3= (1 + 𝑓)
𝑇4
𝑇3 𝑉3
𝑉4 (10)
Stream thrust function at combustor exit conditions
𝑆𝑎4 = 𝑉4 (1 +𝑅𝑇4
𝑉42 ) (11)
Expansion Components (4-10):
Temperature at engine exit
𝑇10 = 𝑇4 {1 − 𝜂𝑒 [1 − (𝑃10
𝑃0 𝑃0
𝑃4)
𝑅
𝐶𝑝𝑒]} (12)
Velocity at engine exit
𝑉10 = √𝑉42 + 2𝐶𝑝𝑒(𝑇4 − 𝑇10) (13)
Stream thrust function at engine exit condition
𝑆𝑎10 = 𝑉10 (1 +𝑅𝑇10
𝑉102 ) (14)
Ratio of area at engine exit to area at free stream
entrance
𝐴10
𝐴0= (1 + 𝑓)
𝑃0
𝑃10
𝑇10
𝑇0
𝑉0
𝑉10 (15)
Overall Engine Performance Measures
Specific thrust 𝐹
𝑚0̇= (1 + 𝑓)𝑆𝑎10 − 𝑆𝑎0 −
𝑅𝑇0
𝑉0(
𝐴10
𝐴0− 1) (16)
Specific fuel consumption
𝑆 =𝑓𝐹
𝑚0̇
(17)
Specific impulse
𝐼𝑠𝑝 = (ℎ𝑃𝑅
𝑔0𝑉0) 𝜂0 (18)
Overall efficiency
𝜂0 =𝑉0
ℎ𝑃𝑅𝑆 (19)
Thermal efficiency
𝜂𝑡ℎ =[(1+𝑓)
𝑉102
2 ]−
𝑉02
2
𝑓ℎ𝑃𝑅 (20)
Propulsive efficiency
𝜂𝑃 =𝜂0
𝜂𝑡ℎ (21)
For getting successful combustion in combustor, air entered in combustor must has a temperature higher than an
ignition temperature of corresponding fuel. Ignition
temperature of fuel is defined as a temperature at which fuel
has no need to any spark for getting ignite. IT of fuel is very
important thing in our project because at moment of starting
of scramjet engine, air flow entered in intake has very low
speed of Mach 3.5, so it will has relatively low temperature
at intake of combustor. Ignition temperature of various fuels
are given below and taken from [13, 14, 15] :
Fuel IT (K)
Hydrogen 845.15
Methane 810.15
Ethane 745.15
JP-10 518.15
JP-7 514.15
Hexane 498.15
Octane 479.15
Scramjet engine is nothing but the supersonic combustion ramjet. So after combustion of fuel, burned
gases must have speed higher than Mach 1 at end of
combustor in case of scramjet engine. As we seen in
equations given above, combustor exit velocity is highly
depend on combustor entry velocity i.e. 𝑉3 and fuel-to-air
ratio (f). combustor exit temperature is depend on combustor
entry temperature (𝑇3), combustor entry velocity (𝑉3), fuel-
to-air ratio (f), combustor ext velocity (𝑉4) and heat of
reaction of fuel. Here parameters 𝑉3 & 𝑇3 we can control by proper intake design. So ultimately, Mach No. at combustor
exit (𝑀4) is depend on intake design as well as fuel-to-air
ratio (f) and heat of reaction of fuel(hPR). Kristen Roberts
[12] has shown effect of fuel-to-air ratio (f) on combustor
exit Mach No(𝑀4). He showed that as we decrease the
value of fuel-to-air ratio (f) from value stoichiometric fuel-
to-air ratio (𝑓𝑠𝑡) of corresponding fuel, combustor exit Mach
No(𝑀4) will goes to increase.
stoichiometric fuel-to-air ratio (𝑓𝑠𝑡 ) of various fuels are
given below and calculated from (22) taken from [12] :
𝑓𝑠𝑡 =36𝑥+3𝑦
103(4𝑥+𝑦) where the fuel s represented in the form of
𝐶𝑥𝐻𝑦 (22)
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 262
Table 1: Stoichiometric fuel-to-air ratio (𝑓𝑠𝑡 ) of various listed fuels
Fuel Type Chemical
Formula
𝒇𝒔𝒕
Hydrogen 𝐻2 0.0291
Methane 𝐶𝐻4 0.0583
Ethane 𝐶2𝐻6 0.0624
JP-10 𝐶10𝐻16 0.0707
JP-7 𝐶12𝐻25 0.0674
Hexane 𝐶6𝐻14 0.0659
Octane 𝐶8𝐻18 0.0664
There is some limit for variation in fuel-to-air ratio,
equivalence ratio (∅) is used as a limiting parameter for that.
Equivalence ratio is defined as a ratio of fuel-to-air ratio
used (f) to the stoichiometric fuel-to-air ratio (𝑓𝑠𝑡 ) .
∵ ∅ =𝑓
𝑓𝑠𝑡
(23)
Heiser and pratt [12] stats that a general guidelines for
the equivalence ratio is from 0.2 to 2 for “combustion to
occur within a useful timescale.”
Heats of reaction of corresponding fuels per mass are
given below and taken from [1, 16, 17]
Table 2: Heat of reaction of various listed fuels.
Fuel Type 𝒉𝑷𝑹 (
𝑲𝑱
𝑲𝒈 𝑭𝒖𝒆𝒍)
Hydrogen 119954
Methane 50010
Ethane 47484
JP-10 42100
JP-7 43903
Hexane 45100
Octane 44786
As we have seen in the equations given above, the whole performance of the scramjet engine is dependent on
the performance of the inlet. The performance of the engine
depends on how efficiently can inlet compress the intake air
and how much pressure recovery the intake can achieve.
Compression and pressure recovery of intake air depend on
the structure of oblique shocks, which directly depend on the
configuration of the inlet such as the number of ramps
present in the inlet and angles between each pair of adjacent
ramps. So proper design of inlet according to an application
would give an expected performance of the scramjet engine.
1.3 One- Dimensional Flow Analysis
1.3.1 Oblique Shock Wave Relations
As we discussed, in hypersonic intake, air is
compressed by multiple oblique shock waves. So for getting
idea about various flow parameters at the end of intake and
shock deflection angle at every ramp, oblique shock wave
relations are used for this purpose. Flow properties at
downward side of oblique shock wave are calculated by
flow properties at upward side and flow turning angle [3].
First, relation between M-𝜃-𝛽 is given by (24) [3]:
𝑡𝑎𝑛𝜃 = 2𝑐𝑜𝑡𝛽𝑀1
2 sin2 𝛽−1
𝑀12(𝛾+𝑐𝑜𝑡2𝛽)+2
(24)
Where θ is turning angle, 𝑀1 is Mach number at upward
side and 𝛽 is shock deflection angle
Other flow properties at downward side are calculated by
(25-30)given below [3]:
𝑀𝑛1 = 𝑀1𝑠𝑖𝑛𝛽 (25)
𝑀𝑛2 = √1+[(𝛾−1)/2]𝑀𝑛1
2
𝛾𝑀𝑛12 −(𝛾−1)/2
(26)
𝑀2 =𝑀𝑛2
sin(𝛽−𝜃) (27)
𝑃2
𝑃1= 1 +
2𝛾
𝛾+1(𝑀𝑛1
2 − 1) (28)
𝜌2
𝜌1=
(𝛾+1)𝑀𝑛12
2+(𝛾−1)𝑀𝑛12 (29)
𝑇2
𝑇1=
𝑃2
𝑃1.
𝜌1
𝜌2 (30)
II. LITERATURE REVIEW
By tremendous research during the decade of 1950 to
1960, it was very clear that if we want to eliminate the
limitations of rocket and also want to get more performance than a rocket, then the scramjet or air-breathing propulsion
is the best choice[1]. In an air-breathing engine for M >1,
there are two options available: ramjet engine and scramjet
engine but, when operating speed is M >5, then ramjet
engine cannot work efficiently due to high losses in intake
and very high flow temperature in combustor[1]. Fry [2]
showed the efficient operating Mach number range for
different propulsion systems with two fuel options:
hydrogen and hydrocarbons. Basic oblique and normal
shock relations are very useful in inlet design. Anderson [3]
states equations of different flow properties based on upstream conditions. Luu Hong Quan et.al.[4] carried out
CFD analysis on hypersonic inlets with different No. of
ramp against a wide range of Mach number (M=5-10) and
analyzed the different flow parameters for all inlets. They
proved that an inlet with three ramps is the best choice for a
given range of Mach number The performance of the
hypersonic inlet also depends on various operating
conditions. Augusto F.Moura and Mauricio A.P. Rosa[5]
carried out CFD analysis of hypersonic inlet at different
operating conditions. Operating conditions that are varied
are: operating height, angle of attack, and operating speed.
And analyzed the different flow parameters. Except No. of the ramp, ramp angles and other geometrical changes in inlet
geometry also impress a huge impact on flow parameters of
air passing through inlet. Atulya Sethi [6] carried out CFD
analysis on hypersonic inlets with different combinations of
No. of ramp and ramp angles at particular Mach number
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 263
And analyzed the different flow parameters. He also
compared the values of various flow parameters with values obtained by theoretical equations. Murugesan et.al. [7] ]
carried out CFD analysis on hypersonic inlets with different
geometrical changes like inlets with different No. of the
ramp, inlets with same No. of the ramp but varied ramp
angles, inlet with different cowl angle and also carried out
an analysis on axisymmetric inlets. By analyzing different
flow parameters for various inlet geometries, they proved
that an inlet with four ramps gives better results than other
models for given choices of Mach number Azam che Idris
et.al. [8] performed experimental analysis on the hypersonic
inlet in a laboratory with different angles of attack and
compared the value of various flow parameters with the value obtained by CFD analysis. Murthy, S.N.B, and
Curran. E.T [9] have shown performance data of different
inlet designs at different Mach number and also discussed
major issues related to the hypersonic inlet. Devendra sen
et.al.[10] carried out CFD analysis of hypersonic inlet for
combined cycle engine for a wide range of Mach number
(M=5-8) and found that four ramp inlet is best the choice in
terms of pressure recovery and adiabatic efficiency for a
given range of Mach number For getting continuous
operation at design range of Mach number, inlet must not
transfer on unstart state at any Mach number within a range. Qi-Fan Zhang et.al. [11] have shown the process of inlet
unstart at low speed, design, and over speed mode.
Research reviews presented above are basically about
research works of the hypersonic inlet with 𝑀 ≥ 5. So now,
when hypersonic inlet has analyzed against very low Mach
number, at that time, there are many problems have raised,
which we have to face during operation. Kristen Roberts
[12] has shown the problems which are raised, when we
tasted hypersonic inlet against very low Mach number and
also stated some remedies for eliminating those problems and getting good performance. So overall, none of the
research was carried out up to now, which analyzed the
behavior of hypersonic inlet against very low Mach number
and study about different flow parameters and performance
parameters for various inlet geometries. This study involves
the CFD analysis and technical understanding of various
geometries of hypersonic inlets tested against lower starting
Mach number (M=3.5). The main objective of this study is
to analyze, whether predefined geometries will start against
lower speed Mach number (M=3.5) or not? if not then
investigate those geometric model(s) technically and find out the reason behind them. In the following sections, the
paper will deal with fuel selection, analysis of flow
parameters at different sections of a scramjet engine,
performance parameters, and efficiencies for different
geometries of the inlet which are already tested successfully
against lower starting Mach number and compare it with
each other.
III. METHODOLOGY
For performing 2-D CFD analysis, first I choose a total
of 11 geometries with different combinations of a number of
ramp and ramp angles. Here I took the same isolator length
for all the geometries. All the geometries are designed at
Mach 6 because, after started at a lower starting Mach
number (M=3.5), a vehicle will cruise continuously at
hypersonic speed i.e. Mach 6. So if we design an inlet at
Mach 3.5, then it cannot work with its maximum efficiency
at Mach 6 in which the missile will cruise most of the time.
Different geometric models are given below:
Model :1
Number of ramp 2
Ramp angles (Degree) 8,7.5
Ramp lengths (mm) 700,704.6
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model :2
Number of ramp 2
Ramp angles (Degree) 8,8
Ramp lengths (mm) 800,767.13
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:3
Number of ramp 2
Ramp angles (Degree) 8.5,8
Ramp lengths (mm) 700,651.32
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:4
Number of ramp 2
Ramp angles (Degree) 9,8
Ramp lengths (mm) 700,633.48
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:5
Number of ramp 3
Ramp angles
(Degree)
7.6,7,6
Ramp lengths (mm) 700,278.75,348.37
Cowl angle
(Degree)
0
Isolator length (mm) 1200
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
ISSN No:-2456-2165
IJISRT21OCT269 www.ijisrt.com 264
Model:6
Number of ramp 3
Ramp angles (Degree) 8.15,7,6
Ramp lengths (mm) 700,267.56,373.34
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:7
Number of ramp 3
Ramp angles (Degree) 8.3,7.3,6
Ramp lengths (mm) 700,278.57,381.1
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:8
Number of ramp 3
Ramp angles (Degree) 8.5,7,6
Ramp lengths (mm) 700,267.07,303.68
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:9
Number of ramp 4
Ramp angles
(Degree)
7,6,5,4
Ramp lengths (mm) 800,331.17,157.7,345.78
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:10
Number of ramp 4
Ramp angles (Degree) 7,6.5,5,4.5
Ramp lengths (mm) 800,323.11,152.76,315.86
Cowl angle (Degree) 0
Isolator length (mm) 1200
Model:11
Number of ramp 4
Ramp angles (Degree) 8,7,6.5,5
Ramp lengths (mm) 800,318.5,142.13,243.6
Cowl angle (Degree) 0
Isolator length (mm) 1200
3.2 Free stream condition
Here it is assumed that hypersonic vehicle is cruise in
constant dynamic pressure trajectory, which has dynamic
pressure of 47880 𝑁/𝑚2. This value is directly taken from
reference [12]. By taken dynamic pressure and Mach
number as input values, we can calculate corresponding
pressure and temperature at particular height. Flow
properties at each Mach number on constant dynamic
pressure trajectory are given below:
Table 3: Pressure and temperature of air at different Mach
number for same dynamic pressure
Mach number
Height (m) 𝑇0 (𝐾) 𝑃0 (𝑃𝑎)
3.5 19936.97 216.65 5582
4 21646.90 218.22 4275
4.5 23167.85 219.73 3377
5 24539.45 221.09 2736
5.5 25786.08 222.33 2260
6 26929.08 223.47 1900
There are many other parameters used in stream thrust
analysis, some of them has constant value throughout the
analysis and some of them has assumed value. List of these
values are given below and directly taken from reference
[12]:
Table 4: List of constant parameters used in stream thrust
analysis
Constants [12]
𝐶𝑝𝑐 1090 𝐽/𝑘𝑔𝐾
R 289.3 (
𝑚
𝑠)
2
/𝐾
𝐶𝑝𝑏 1510 𝐽/𝑘𝑔𝐾
𝐶𝑝𝑒 1510 𝐽/𝑘𝑔𝐾
ℎ𝑓 0.00
𝑔0 9.81 𝑚/𝑠2
Table 5: List of assumed parameters used in stream thrust
analysis
Assumed values [12]
𝑉𝑓𝑥/𝑉3 0.50 𝑇0 222.0 K
𝑉𝑓/𝑉3 0.50 𝑃10/𝑃0 1.40
𝐶𝑓
∗ 𝐴𝑤/𝐴3
0.10 𝛾𝑐 1.362
𝜂𝑐 0.90 𝛾𝑏 1.238
𝜂𝑏 0.90 𝛾𝑒 1.238
𝜂𝑒 0.90
3.2 Computational Domain
Fig. 3.2.1: Computational fluid domain for 2 ramp inlet
geometry
Volume 6, Issue 10, October – 2021 International Journal of Innovative Science and Research Technology
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Fig. 3.2.2: Computational fluid domain for 3 ramp inlet
geometry
Fig. 3.2.3: Computational fluid domain for 4 ramp inlet
geometry
Here as shown in figures given above, inlet geometry
is bounded by the main rectangular fluid domain which is further divided into sub-domains. Here I generated a
separate sub-domain for all the ramps and also for the
isolator, for catching shocks and their interaction and also
for getting better accuracy of results. I also generated sub-
domain at an upper and lower portion of inlet geometry for
catching flow spillage happened at off-design conditions.
3.3 Meshing
For carried out 2-D simulation over inlet geometry, a
structured grid with quadrilateral cells is made. All the sub-
domains of geometry consist of a structured grid. There are more than 32000 nodes in each geometric model of the inlet.
Sub-domains of ramp and isolator consist of fine mesh for
capturing shocks in a better way, while upper and lower sub-
domain of inlet geometry consists of medium mesh.
(a)
(b)
(c)
Fig. 3.3.1: Mesh at different sections of 4 ramp inlet design.
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ISSN No:-2456-2165
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IV. RESULTS AND DISCUSSION
Fig. 4.1:Pressure contour of model 1 at Mach3.5 Fig. 4.2:Temperature contour of model 1 at Mach 3.5
Fig. 4.3:Velocity contour of model 1 at Mach 3.5
Fig. 4.4:Pressure contour of model 2 at Mach3.5 Fig. 4.5:Temperature contour of model 2 at Mach 3.5
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Fig. 4.6:Velocity contour of model 2 at Mach 3.5
Fig. 4.7:Pressure contour of model 3 at Mach3.5 Fig. 4.8:Temperature contour of model 3 at Mach 3.5
Fig. 4.9:Velocity contour of model 3 at Mach 3.5
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Fig. 4.10:Pressure contour of model 4 at Mach3.5 Fig. 4.11:Temperature contour of model 4 at Mach3.5
Fig. 4.12:Velocity contour of model 4 at Mach 3.5
Fig. 4.13:Pressure contour of model 5 at Mach3.5 Fig. 4.14:Temperature contour of model 5 at Mach3.
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Fig. 4.15:Velocity contour of model 5 at Mach 3.5
Fig. 4.16:Pressure contour of model 6 at Mach3.5 Fig. 4.17:Temperature contour of model 6 at Mach3.5
Fig. 4.18:Velocity contour of model 6 at Mach 3.5
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Fig. 4.19:Pressure contour of model 7 at Fig. 4.20:Temperature contour of model 7 at
Mach3.5 Mach 3.5
Fig. 4.21:Velocity contour of model 7 at Mach 3.5
Fig. 4.22:Pressure contour of model 8 at Fig. 4.23:Temperature contour of model 8 at
Mach3.5 Mach 3.5
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Fig. 4.24:Velocity contour of model 8 at Mach 3.5
Fig. 4.25:Pressure contour of model 8 at Fig. 4.26:Temperature contour of model 9 at
Mach3.5 Mach 3.5
Fig. 4.27:Velocity contour of model 9 at Mach 3.5
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Fig. 4.28:Pressure contour of model 10 at Fig. 4.29:Temperature contour of model 10 at
Mach3.5 Mach 3.5
Fig. 4.30:Velocity contour of model 10 at Mach 3.5
Fig. 4.31:Pressure contour of model 11 at Fig. 4.32:Temperature contour of model 11 at
Mach3.5 Mach 3.5
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Fig. 4.33:Velocity contour of model 11 at Mach 3.5
Here in all two ramps design i.e. model 1,2,3&4, flow
spillage is clearly seen, as these simulations are carried out at Mach 3.5 i.e. below the design Mach number. All the
shocks are attached throughout the whole inlet body. Here
we can clearly see that shocks are reflected inside the
isolator only up to some part of the total length, so it will not
affect the combustion process happening inside the
combustor. Flow separation has not happened inside the
isolator because there is no shocks interaction formed inside
it. As per the cases of two ramp designs, flow spillage also
happened in the cases of three ramp designs. In the case of
model 5,6&7, all the shocks are attached throughout the
whole inlet body but in model 8, shock is detached near the end part of the third ramp. This shock detachment happened
because of the comparatively larger deflection angle of
ramps. Here no shock penetration happened inside the
isolator, so the combustor will get flow with uniform flow
properties. There is no flow separation happened in the case
of model 5,6&7 but due to shock detachment, significant
flow separation is visible in the case of model 8. As same as
previous cases, we can clearly see the flow spillage also in
four ramp designs. . In the case of models 9&10, shocks are
attached throughout the inlet body but in the case of model
11, shock detachment has happened. Shock penetration
inside the isolator has not happened also in four ramp designs. Minor flow separation is visible in the case of
models 9&10 because of somewhat larger ramp angles
according to intake airflow velocity.
In all three types of design i.e. 2 ramps, 3 ramps &4
ramps intake designs, as ramp angles are increase,
temperature and pressure are going to increase while
velocity is going to decrease because as the ramp angles go
higher, oblique shocks will become more stronger. The
cases in which shock detachment happened, a large velocity
drop at a place of detachment is shown in those corresponding cases. So pressure recovery is also very low
in those cases. Isolator helped to increase pressure and
temperature up to the required value. The role of the isolator
here in this type of crucial case, where some required values
of pressure and temperature must be needed is so important.
Values of different flow parameters at various stations
and performance parameters of scramjet engine at Mach 3.5
for all models are given below:
Table 6: List of different flow and performance parameters obtained at the end of stream thrust analysis for Mach 3.5
Model No. No. of
Ramp
Ramp Angles 𝑻𝟑
(K)
𝑽𝟑
(𝒎
𝒔𝒆𝒄)
𝑷𝟑
(Mpa)
𝑻𝟒
(K)
𝑽𝟒
(𝒎
𝒔𝒆𝒄)
𝑴𝟒
1 2 (8,7.5) 460 725 1.35 - - -
2 2 (8,8) 490 660 1.65 1185 652.84 1.0004
3 2 (8.5,8) 490 655 1.70 1160.4 649.94 1.0018
4 2 (9,8) 512 625 1.86 1033.2 611.875 1.0041
4 2 (9,8) 512 625 1.86 1036.9 611.875 1.0024
5 3 (7.6,7,6) 487 662 1.61 1192 655.20 1.0011
6 3 (8.15,7,6) 510 635 1.80 1081.1 623.50 1.0003
6 3 (8.15,7,6) 510 635 1.80 1060.1 622.585 1.0087
7 3 (8.3,7.3,6) 512 630 1.85 1058.1 617.683 1.0017
7 3 (8.3,7.3,6) 512 630 1.85 1057 617.5 1.0019
8 3 (8.5,7,6) 575 535 1.875 1094 523.765 0.8353
8 3 (8.5,7,6) 575 535 1.875 1097.7 523.765 0.8339
9 4 (7,6,5,4) 487 663 1.40 1196.8 656.383 1.0009
10 4 (7,6.5,5,4.5) 513 620 1.63 1034.2 611.875 1.0037
10 4 (7,6.5,5,4.5) 513 620 1.63 1037.8 611.875 1.0019
11 4 (8,7,6.5,5) 575 530 2.1 1094 518.87 0.8275
11 4 (8,7,6.5,5) 575 530 2.1 1097.7 518.87 0.8216
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𝑻𝟏𝟎
(K)
𝑽𝟏𝟎
(𝒎
𝒔𝒆𝒄)
𝑭/�̇�
(𝑵 𝒔/𝒌𝒈)
Sp.fuel
consumption
(𝒌𝒈
𝑵 𝒔)
Fuel Fuel to
Air
Ratio
(f)
𝜼𝟎 𝜼𝒕𝒉 𝜼𝑷 Isp
(sec)
Possible
or Not
- - - - Octane - - - - - Not
500 1579.8 633.23 4.264× 10−5 Octane 0.027 0.5325 0.6322 0.8423 2390.6 Yes
487.225 1565.8 616.78 4.215× 10−5 Octane 0.026 0.5386 0.6360 0.847 2418 Yes
428.14 1483.3 521.65 3.834× 10−5 Octane 0.02 0.5922 0.6763 0.8757 2658.6 Yes
426.66 1486 523.93 3.817× 10−5 Hexane 0.02 0.5907 0.6753 0.8748 2670.5 Yes
504.44 1582.8 637.21 4.3× 10−5 Octane 0.0274 0.5281 0.6274 0.8416 2370.8 Yes
450.12 1514.7 556.958 3.95× 10−5 Octane 0.022 0.5748 0.6650 0.8644 2580.5 Yes
441.384 1502 542.22 3.873× 10−5 Hexane 0.021 0.5822 0.6701 0.8688 2632 Yes
438.81 1500.6 540.676 3.884× 10−5 Octane 0.021 0.5846 0.6725 0.8693 2624.5 Yes
438.337 1500 539.582 3.854× 10−5 Hexane 0.0208 0.585 0.6728 0.8694 2644.7 Yes
- - - - Octane 0.02 - - - - Not
- - - - Hexane 0.02 - - - - Not
517.051 1576 631.3 4.372× 10−5 Octane 0.0276 0.5194 0.6141 0.8458 2331.8 Yes
436.9 1476 514.206 3.89× 10−5 Octane 0.02 0.5838 0.663 0.8806 2620.9 Yes
438.45 1478 516.47 3.872× 10−5 Hexane 0.02 0.5823 0.6619 0.8797 2632.5 Yes
- - - - Octane 0.02 - - - - Not
- - - - Hexane 0.02 - - - Not
Here I used octane and hexane as fuel according to the
airflow temperature I got at the exit of the isolator. So
according to the allowable equivalence ratio as mentioned in
the previous section, the allowable range for variation of
fuel-to-air ratio is 0.02-0.0664 for octane and 0.02-0.0659
for hexane
In model 1, airflow temperature at the exit of isolator
did not reach up to the ignition temperature of fuels, so model 1can not work in the condition of lower starting Mach
number. In models 8 & 11, even at the lowest possible fuel-
to-air ratio, the Mach number at the combustor exit did not
reach above Mach 1. So model 8 & 11 also cannot work in
the condition of lower starting Mach number, as must be
greater than 1 in case of the scramjet engine. Here I took the
best cases from all three types of intake design i.e. 1-ramp,
2-ramp & 3-ramp design for further analysis on the basis of
the value of 𝐹/�̇�. So that models 2,5 & 9 are selected for further analysis at Mach 6.
Fig. 4.45:Pressure contour of model 2 at Fig. 4.46:Temperature contour of model 2 at
Mach 6 Mach 6
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Fig. 4.47:Velocity contour of model 2 at Mach 6
Fig. 4.48:Pressure contour of model 5 at Fig. 4.49:Temperature contour of model 5 at
Mach 6 Mach 6
Fig. 4.50:Velocity contour of model 5 at Mach 6
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Fig. 4.51:Pressure contour of model 9 at Fig. 4.52:Temperature contour of model 9 at
Mach 6 Mach 6
Fig. 4.53:Velocity contour of model 9 at Mach 6
Here all three designs i.e. model no 2,5 & 9 operating
at design Mach number (M= 6), so that all the shocks have
impinged exactly at the cowl tip. Due to shock on lip
condition exist, there is no flow spillage has happened in these cases. The boundary layer at the vehicle forebody and
ramp walls are thinner than the boundary layer at Mach 3.5.
It is clearly visible that the shock train is propagating inside
the isolator so that pressure and temperature are increased
and velocity is decreased at the end of the isolator due to
flow passes through the continuous shock train. There is
minor flow separation at the upper wall of the isolator is
visible in case of model numbers 5&9
As shown in the figures, temperature and pressure at
end of the isolator are quite higher in 3 & 4 ramp designs
than in 2-ramp design, while velocity is higher in 2-ramp design because of the higher pressure ratio of 3 & 4 ramp
inlet designs. Whereas the performance of 3 & 4 ramp inlet
designs in terms of flow parameters is quite similar to each
other. Shock train propagation inside the isolator is clearly
visible in the graphs. Values of different flow parameters at
various stations and performance parameters of scramjet
engine at Mach 3.5 for all models are given below:
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Table 7: List of different flow and performance parameters obtained at the end of stream
thrust analysis for Mach 6
Model
No.
No. of
Ramp
Ramp Angles 𝑻𝟑
(K)
𝑽𝟑
(𝒎
𝒔𝒆𝒄)
𝑷𝟑
(Mpa)
𝑻𝟒
(K)
𝑽𝟒
(𝒎
𝒔𝒆𝒄)
𝑴𝟒
2 2 (8,8) 632 1490 2.70 2164.6 1559 1.7675
5 3 (7.6,7,6) 780 1380 4 2318.2 1443.9 1.582
9 4 (7,6,5,4) 800 1380 3.75 2337 1444 1.5755
𝑻𝟏𝟎
(K)
𝑽𝟏𝟎
(𝒎
𝒔𝒆𝒄)
𝑭/�̇�
(𝑵 𝒔/𝒌𝒈)
Sp.fuel
consumpt
ion
(𝒌𝒈
𝑵 𝒔)
Fuel Fuel to
Air
Ratio
(f)
𝜼𝟎 𝜼𝒕𝒉 𝜼𝑷 Isp
(sec)
Possible
or Not
731.42 2600 1027.4 6.462×10−5
Octane 0.0664 0.6117 0.6848 0.8933 1577.3 Yes
743.2 2615.6 1044.6 6.356×10−5
Octane 0.0664 0.6219 0.6996 0.8890 1603.6 Yes
755.637 2619.2 1048.8 6.33×10−5
Octane 0.0664 0.6245 0.7030 0.8883 1610.3 Yes
Herein all the cases, I used stoichiometric fuel-to-air ratio for measuring performance parameters. Graphs of performance
parameters of these selected models for the whole Mach number range i.e. 3.5 to 6 are given below:
Fig.4.57: Thrust generated by selected intake models at different mach numbers.
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
3 3.5 4 4.5 5 5.5 6
Th
rust
/(K
g/s
)
Mach Number
Thrust generated by selected intake models at different
mach numbers
Intake Model:2
Intake Model:5
Intake Model:9
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Fig.4.58: Thermal Efficiency of selected intake models at different mach numbers
Fig.4.59: Total efficiency of selected intake models at different mach numbers
0.58
0.6
0.62
0.64
0.66
0.68
0.7
0.72
3 3.5 4 4.5 5 5.5 6
Th
erm
al
Eff
icie
ncy
Mach Number
Thermal Efficiency of selected intake models at
different mach numbers
Intake Model:2
Intake Model:5
Intake Model:9
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
3 3.5 4 4.5 5 5.5 6
Tota
l E
ffic
ien
cy
Mach Number
Intake Model:2
Intake Model:5
Intake Model:9
Total efficiency of selected intake models at different
mach numbers
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Fig.4.60: Propulsive efficiency of selected intake models at different mach numbers
Fig.4.61: Isp of selected intake models at different mach numbers
V. CONCLUSION
From figures given in the previous section, for
hypersonic intake geometry with no moving parts in a
condition of lower starting Mach number, intake with 2
ramps has the highest performance in terms of thrust
generation, Isp & efficiencies among three selected models at lower Mach number i.e. Mach 3.5 for our case of
analysis and lowest performance at Mach number 6, while
intake with four 4 has the highest performance in terms of
thrust generation, Isp & efficiencies among three selected
models at Mach number 6 and lowest performance at lower
Mach number 3.5. The reason behind the performance
degradation of 4 ramp intake at lower Mach number is the
strong shock generation at the entrance of the isolator, which
decreases pressure recovery up to a large extent. We have
also seen that designing four ramp intakes for lower starting Mach numbers is very difficult as the intake unstart
problem is predominant in this case. Intake with 3 ramps has
a quite good performance at both lower and designed Mach
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
3 3.5 4 4.5 5 5.5 6
Pro
pu
lsiv
e E
ffic
ien
cy
Mach Number
Intake Model:2
Intake Model:5
Intake Model:9
Propulsive efficiency of selected intake models at
different mach numbers
1550
1650
1750
1850
1950
2050
2150
2250
2350
2450
3 3.5 4 4.5 5 5.5 6
Isp
(se
c)
Mach number
Isp of selected intake models at different mach
numbers
Intake Model:2
Intake Model:5
Intake Model:9
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numbers. Even at Mach 6, intake with 3 ramps has
performance very similar to intake with 4 ramps. So we can say that intake with 3 ramps is the best choice for lower
starting Mach number condition. If we talk about fuel
selection, then octane is suitable fuel when hypersonic
intake with lower starting Mach number scenario is to be
considered as it has a lower self-ignition temperature which
plays a very important role in this type of scenario.
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